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Nonlinear Self-Adjointness and Generalized Conserved Quantities of the Inviscid Burgers’ Equation with Nonlinear Source

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Abstract

The conservation laws of the inviscid Burgers’ equation under consideration have been studied recently using the concept of quasi self-adjointness and self-adjointness. These two concepts have been extended to the notion of nonlinear self-adjointness to enable more conservation laws of differential equations, that are not achievable through them, be constructed. We explore this avenue in the present study and establish the generalized nonlinearly self-adjoint condition for the inviscid Burgers’ equation. This condition not only gives rise to new nontrivial independent conserved vectors, but also includes results of previous work as a particular case.

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Notes

  1. Except for \(\zeta =\alpha ^{k}\) under \(X_{1}\) and \(\zeta =\beta ^{k}\) under \(X_{2}\), \(k\in \mathbb {R}.\)

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Authors and Affiliations

  1. Deanship of Educational Services, Qassim University, Buraydah, Saudi Arabia

    Muhammad Alim Abdulwahhab

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  1. Muhammad Alim Abdulwahhab
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Abdulwahhab, M.A. Nonlinear Self-Adjointness and Generalized Conserved Quantities of the Inviscid Burgers’ Equation with Nonlinear Source. Int. J. Appl. Comput. Math 3, 963–970 (2017). https://doi.org/10.1007/s40819-016-0146-y

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